Interferometeric lightning ranging system

ABSTRACT

The lightning ranging system for determining distance between a lightning discharge and an airborne object includes a receiver on the airborne object adapted to receive electromagnetic radiation signals generated by a lightning discharge along both a direct and a surface reflected path. Signal processing apparatus is interconnected with the receiver for determining the difference in the time of arrival of the direct and reflected signals. A computer is provided to calculate the range of the lightning discharge from the difference in the time of arrival of the direct and reflected signals. In a preferred embodiment, the signal processing apparatus is digital and includes at least a 10-bit analog-to-digital converter with at least a 36 megahertz sampling rate.

BACKGROUND OF THE INVENTION

The present invention relates to lightning detection, and moreparticularly to determining the range between an airborne object and alightning discharge.

Thunderstorms are dangerous to aircraft because of many factors,including violent turbulence, lightning strikes to the aircraft andhail. Increasing use of modern non-conducting materials on aircraftcontaining sophisticated electronics and fly-by-wire control systemsmakes them particularly sensitive to thunderstorm electrical hazards.

At present, there are two methods for locating thunderstorms so thatthey may be avoided by aircraft. A traditional method for avoidingthunderstorms involves the use of radar. Radar, however, has certaininherent limitations restricting its effectiveness. While with anunobstructed view radar can see heavy rain at ranges of 100 miles ormore and lighter rain when closer, radar signals are attenuated byprecipitation from closer clouds which mask more distant rain. Moreover,rain per se does not necessarily imply the presence of thunderstorms,nor do all thunderclouds produce heavy rain; sometimes they produce norain. In addition, many aircraft, military as well as civilian(particularly single engine) have no convenient location for radarantennas. Radar also requires appreciable electrical power which may notbe available on smaller general avaiation airplanes. Because of therelatively high expense of radar equipment, radar is not used on 95% ofthe approximately 200,000 general aviation light aircraft in the UnitedStates. Furthermore, the thin wings and possible use of nosecompartments for armaments or electronic devices are factors which mayprevent the use of radar on some military aircraft.

An alternative to radar for storm avoidance is to use radio frequency(RF) emissions from lightning for determining the occurrence andposition of lightning which must be associated with thunderclouds.Approximately 10 years ago, a device known as the Stormscope wasdeveloped to present a real time display for pilots so that lightningregions could be avoided. This device uses the well-establishedcrossed-looped sensor technique to determine the azimuth of lightningand estimates range from signal intensity. That is, the Stormscopeassumes that all lightning flashes are of equal strength with rangedetermined by the attenuation in the received signal. With thisapparatus, strong flashes appear too near and weak flashes appear toofar away. Both theoretical and empirical evaluations of the Stormscopeindicate approximately a factor of two accuracy.

It is therefore an object of the present invention to provide alightning ranging system having higher accuracy than the Stormscope andto eliminate the inherent limitations of radar discussed above.

It is yet another object of the invention to provide a lightning rangingsystem which is inexpensive as compared to radar systems.

Yet another object of the invention is lightning ranging equipment whichutilizes existing electronic components.

SUMMARY OF THE INVENTION

These and other objects of the invention are achieved by a lightningranging system for determining distance between a lightning discharge atan altitude H₁ and an airborne object at an altitude H₂ including areceiver on the airborne object adapted to receive electromagneticradiation signals generated by a lightning discharge along both a directand a surface reflected path. Signal processing apparatus isinterconnected with the receiver for determining the difference in thetime of arrival of the direct and reflected signals. A computer isprovided for calculating the distance from the difference in the time ofarrival of the direct and reflected signals. It is preferred that thesignal processing be done digitally, utilizing a 10-bitanalog-to-digital converter with a 36 megahertz sampling rate. Thesignal processing apparatus computes the spectrum of the receivedlightning discharge signal and then takes the logarithm of the spectrum.The Fourier transform of the logarithm of the spectrum is computed, theFourier transform includes a sharp peak indicating the difference intime of arrival. The difference in time of arrival is then used tocalculate the distance from the airborne object to the lightningdischarge.

BRIEF DESCRIPTION OF THE DRAWING

The invention disclosed herein will be understood better with referenceto the drawing of which:

FIG. 1 is a schematic illustration of the geometry for path differencedetermination;

FIGS. 2 and 3 are graphs of range versus path difference;

FIGS. 4a and 4b are graphs of range versus echo/direct power;

FIGS. 5a, b and c are power spectra of the combined direct and reflectedsignal;

FIG. 6 is a graph of baseband spectrum of lightning with an artificial0.2 microsecond delay;

FIG. 7 is a graph of the autocorrelation function of lightning with anaritificial 0.2 microsecond delay; and

FIG. 8 is a block diagram of the interferometric lightning rangingsystem disclosed herein.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention determines the range of a lightning flash bydetecting the difference in the time of arrival of the direct andreflected electromagnetic signals from the lightning discharge. This"single station" approach is useful when there is insufficientseparation available for cross bearings utilizing two or more antennas.For example, it could be used from a satellite, a mountain peak, a tallbuilding or a ship with a sufficiently tall superstructure or mast.Alternatively, a kite or balloon deployed from a ship or ground stationcould carry a sensor aloft to provide sufficient vertical separation toutilize the proposed ranging technique. The features of the rangingtechnique will first be described qualitatively. To a great extent, thequalitative description relies upon quantitative calculations which willbe presented later. Geometric factors enter first of all in the timedifference that is the basis for ranging. They are also involved, alongwith electromagnetic factors, in the relative strength of the direct andreflected signals. In turn, the time difference and the signal strengthdetermine the specifications for the electronic system.

As stated above, the present invention utilizes a signal reflected fromthe earth's surface in comparison with the direct signal to infer range.The present method may be used both over sea and over land, although thereflected signal from the sea is much stronger. The sea is a remarkablygood mirror for radio waves. The dielectric constant of water is 80 atradio frequencies (in contrast to a value of 1.8 at optical frequencies)and is mainly responsible for the remarkable reflectivity. Theconductivity of sea water further improves the reflectivity, but thatimprovement would not be necessary for the method to be applicable overlarge bodies of fresh water.

The intrinsic reflectivity of land is generally fairly good and thepresent method does not require the extraordinarily high reflectivity ofwater. The main limitation for use over land is roughness of terrain,which can greatly exceed that of the ocean.

Historically, the specular reflection of radio waves from the sea hasbeen more of a hindrance than a help to communication in naval aviation.The interference of direct and reflected waves causes multipath fadingin conventional narrow band radiotelephone or radiotelegraph systems.The problem is serious enough in ship-to-air communication, but is somarked in air-to-air communication to be called "radio holes". Thepresent invention uses this heretofore troublesome interference effectfor lightning ranging. In order to utilize this effect, a wide enoughfrequency band to encompass destructive and constructive interferenceseveral times must be received. The bandwidths that calculations show tobe necessary are not especially demanding upon modern electronicstechnology, being similar to those used in television receivers.

The reflectivity of sea water is always lower for polarization with avertical electric field than for horizontal polarization. Were it notfor the conductivity provided by its salt content, the reflection forvertical polarization would go dwon to zero at an angle of incidence(the Brewster angle) within the range of interest for the presentinvention. These predictions of electromagnetic theory have beenvalidated experimentally for the design of naval avaiation radio, forwhich vertical polarization is therefore preferred, to reduce theseverity of multipath effects. Conversely, horizontal polarization seemspreferable for a lightning ranging system based on reflection. Further,horizontal polarization should favor the more frequent intra-clouddischarges, relative to the less frequent cloud-to-ground andcloud-to-sea discharges. Another advantage of horizontal polarization isdiscrimination against vertically polarized communications signals.

As will become clear below, the longer the range to a lightningdischarge, the shorter will be the time difference between reception ofthe direct and reflected signal. This relationship is in the oppositedirection of the range-time relationship in radar. The time differencein nanoseconds is substantially equal to the difference in the lengthsof the direct and reflected paths, in feet, because the refractive indexof air is not much different from that of free space (where one footcorresponds to 1.02 nanoseconds).

Nevertheless, the slight decrease with altitude of the refractive indexof the atmosphere does have a significant effect. This decrease causesradio waves to travel in curved paths while in the atmosphere. Thiseffect is approximately allowed for by using a fictitious radius for theearth: usually taken to be 4/3 of the actual radius. One then canrepresent radio rays by straight lines in geometric calculations.Calculations have shown that multipath effects from the ionosphere doesnot degrade performance of the present system.

The reflectivity of the sea is extremely high for all radio frequenciesunder consideration. Frequency, however, is very much a factor inassessing the effect of ocean waves. The lower the frequency, the longerthe radio wavelength and the less the effect of sea waves. However, theimpairment of reflectivity is less than one might expect from thecomparison of wave height to radio wavelength. When the grazing angle issmall, the effect of sea waves on reflectivity is greatly diminished.Small grazing angles prevail for the longest ranges. (The grazing angleis the angle between the ray and the plane of the reflecting surface;that is, the tangent plane if the surface is curved. In other words, thegrazing angle is the complement of the angle of incidence measuredbetween the ray and the normal to the surface.)

Signal processing to determine the time difference seems simpler inconcept when the original signal spectrum does not vary widely over theband that is measured. The desirable condition is favored by keeping therelative bandwidth small. A 6 MHz band around 60 MHz is an example. Thecenter frequency is not critical and it would not be costly to provideselectable frequencies to avoid particularly strong man-madeinterference.

A smoothly-varying signal spectrum can be undone by nonuniform responseof the antenna. Making the center frequency much larger than thebandwidth eases the antenna design problem, while offering a choice offrequencies increases the problem. It would be possible to calibrate thesystem with reference to a standard spark. The ability to store such acalibration and to apply it as a correction is one of the advantages ofdigital processing.

The convex sphericity of the earth's surface causes the reflected waveto diverge and thereby be reduced in intensity. This effect is largestfor small grazing angles; that is, for the longest ranges. The relativeintensity of the reflected wave is also slightly reduced because of itslonger length compared to the direct path; this effect has been includedin the calculations but is not very important in cases of interest.

As will be discussed further below, a critical component in the systemof the present invention is the analog-to-digital converter (ADC).Because lightning signals are quite strong, the round-off error of theADC may be the principle source of "noise". At the same time, the ADCmust sample fast enough to encompass the needed bandwidth to identifyclearly the interference pattern between the direct and reflectedsignals. These requirements combine to determine the feasibility ofusing an ADC to permit digital signal processing. The receiverspecifications for use in the present invention have much in common withthose of a conventional television receiver. This fact is expected tolead to significant economies through use of components that are alreadyin mass production. Of course, some additions and modifications areneeded as will be discussed hereinbelow. Protection against grosselectrical overloads is important. Compression of strong but usefulsignals is expected to ease the requirements of the ADC, but must notintroduce irreversible distortion. The compression contemplated hereinwould supplant the slower-acting automatic gain control used intelevision receivers.

The time difference between the directly transmitted electromagneticradiation and the radiation that is reflected from the earth's surfacefrom a lightning discharge, the fundamental indicator of the lightningrange as disclosed herein, will now be discussed. The time difference innanoseconds is practically equal to the difference in the length of thetwo paths in feet. The fact that the refractive index of air is slightlygreater than unity is of negligible consequence in this relation and thereflection from the surface can be assumed to take place without delay.

The gradient in the refractive index of the atmosphere is of somesignificance because the ray paths will be curved. The use of anaritificial earth radius of 4/3 of its actual value is conventional andis adopted here. This correction is not critical in this application andthe reason can best be explained by contrast to those applications whereit is sometimes not accurate enough to assume a 4/3 earth radius. Forexample, communication by narrowly focused beams of microwaves or lightmay require careful aiming to cause the strongest part of thetransmitted beam to be intercepted by the receiving aperture. Ifatmospheric changes cause a different degree of bending, the signalcould be lost entirely. Lightning emits radio waves strongly in alldirection, so that the only effect of an aberrant refractive-indexprofile would be a minor error in the range estimate.

The geometry of the path difference calculation is shown in FIG. 1. InFIG. 1, H1 is the height of the lightning discharge source and H2 is theheight of the airborne object. In this figure, R is chosen to be 4/3 ofactual earth radius as discussed above. The range L shown in FIG. 1 iscomputed by means of the computer program attached hereto as Appendix A.The main check on the correctness of the calculation of the program inAppendix A comes from the approximate formula

    Approximate Path Difference=2*H1*H2/D.

This formula is based upon a flat earth and therefore becomes inaccurateat long ranges. It uses approximations to the trigonometric functionsand for this reason also becomes inaccurate at very short ranges. Thisquantity is calculated in the computer program of Appendix A as thevariable P9.

The more accurate path difference P0 is calculated in the program ofAppendix A in accordance with the geometry shown in FIG. 1, includingthe use of the 4/3 earth radius. Results for P0 are given as the solidcurve in FIGS. 2 and 3, for sample cases. The approximate pathdifference P9 is also shown as a broken line and corresponds to the moreaccurate calculation for intermediate ranges of 10-100 miles, for thesetypical altitudes. The more accurate calculation exhibits the phenomenonof a radio horizon, where the path difference vanishes, at ranges ofabout 300 miles for these examples.

The computer program of Appendix A will compute the more accurate pathdifference P0 when H1 and H2 are known and the time of arrivaldifference is also determined. The height H2 of the airborne object willbe known from instruments on the aircraft such as its altimeter. Whenthe aircraft is above land account will also have to be taken of theterrain height variations. The height, H1, of the lightning dischargemust also be known, and can be estimated from climatological data, theroutine radiosonde balloon soundings obtained by the Weather Services ofthe United States and other countries, and further refined from theprevailing meterological data available from onboard instruments. Theradiosonde data is available for all parts of the United States and muchof the world and pilots can obtain the local temperature profiles overthe radio. Furthermore, thunderstorm research during the last decadeindicates that most of the negative space charge in a thundercloud isconfined to a relatively thin layer in the -10 to -20° C. rangeregardless of height above the ground or location. This may be due tothe presence of mixed phase hydrometeors (supercooled water and ice) ina relatively thin horizontal layer; several of the most prominentelectrification mechanisms depend on the presence of mixed phase orpartially frozen ice pellets. It is also reported that most lightning islocated or originates within this temperature regime.

Thus, knowledge of the atmospheric temperature structure may allow amore accurate than previously expected estimate of the height of thelightning RF source. The atmospheric temperature profile will be knownas described above. Lightning source and airplane heights can beinputted to the device by the pilot. If desired, these quantities canalso be inputted automatically using information from the aircraft'saltimeter and a temperature sensor with appropriate software. Tosummarize, the height of the airplane is known from the airplane'saltimeter. The height of the lightning discharge, H1, is estimated fromthe atmospheric temperature profile. The remaining quantity needed inthe computer program of Appendix A for computing range is the differencein time of arrival between the direct and reflected path signals, whichwill be discussed in the remainder of this specification.

When the ranging system of the present invention is utilized over theocean, the effect of ocean waves on the strength of the reflected signalmust be considered. One expects the sea to be smooth enough for specularreflection when the waves are smaller than the wavelength of theradiation, but the situation is more favorable than that, for thepresent application. For small grazing angles, the effect of waves isproportionately reduced. The description of waves is itselfproblematical. It is commonplace to report the peak-to-trough heightestimated visually. The computer program in Appendix A converts thepeak-to-trough wave height W1 in feet to an rms wave height W in meters.The peak-to-trough height is supposed to be 4.66 times the rms value.Then the expression ##EQU1## is taken as the factor by which thereflected power is reduced by the waves. Here λ is the radio wavelength.The presence of the sine of the grazing angle G is most significant. Itshows that the waves have the least effect when the grazing angle issmall, that is, for the longest ranges. In FIG. 4, a dashed line showsthe results of applying the ocean-wave factor to the horizontalpolarization reflectivity, after that is corrected for divergence andratio of path lengths.

Divergence is another factor which the computer program of Appendix Atakes into account. A sperical reflector functions like a diverging lensand reduces the intensity of the reflection. In radio propagation, thisreduction factor is called divergence. It has the largest effect forsmall grazing angles and is calculated by the approximate formula,

    D1=1/SQR(1+2*R1*R2/(D*R*TAN (G)).

The reflectivity, wave effect and divergence are power ratios. When theyare multiplied together, they give the factor by which the reflectedwave power is expected to be diminished in comparison to the directpower. The square root of this power ratio is taken to give the voltageratio A1. The value of A1 is plotted in FIGS. 4a and 4b for the twocases considered in FIGS. 2 and 3.

One can see that the reflected signal will be relatively very strongunless one is dealing with a rough sea and ranges that may be shorterthan need be considered. The impairment by waves is significant only ifthey are high over a large area; a few very strong waves will not muchreduce the total reflected power.

Antenna considerations for the present invention will now be discussed.A simple way to get uniform azimuthal response to horizontalpolarization is to use a loop lying in the horizontal plane. Ahorizontal loop alos has an agreeable vertical pattern, in that its gainis largest for the smallest grazing angles, which would be encounteredfor the most distant lightning. However, alternative antenna designs,such as combinations of horizontal monopoles or dipoles, could probablybe arranged to give adequate azimuthal coverage for the ranging functionif there were aerodynamic reasons for doing so. Placement of the rangingantenna underneath the aircraft seems natural and would discriminateagainst signals reflected from the ionosphere.

Referring once again to FIGS. 2 and 3, one can see that a usefullightning ranging instrument should be able to deal with path timedifferences in the range of 0.5 to 10 microseconds (path differences of500 to 10,000 feet). Range can be extended to 150 miles or more byevaluating path differences as short as 0.2 microseconds.

The spectrum of the signal produced by lightning is not flat. The signalis strongest at low radio frequencies and decreases (for equalbandwidth) as frequency is increased. The spectrum will be relativelymore constant over a specified bandwidth, the higher the frequency. Itis easier to make a suitable antenna the higher the frequency (i.e.,when the relative bandwidth is smaller).

A reasonably flat signal spectrum is needed because there is no way ofknowing exactly the signal originally radiated from the lightningdischarge. If the intrinsic spectrum can be depended upon to be smooth,one can accurately estimate the path difference from the ripples itintroduces into the spectrum. Suppose, for example, that a 6 MHz bandcentered at 60 MHz is received. The relative bandwidth thus would be 10percent. If the signal power varies as 1/f, the spectrum would look likeFIG. 5a in the absence of a reflection. With an echo time delay of 5microseconds, the spectrum would look that of FIG. 5b; an echo time of0.5 microseconds would give a received spectrum has shown in FIG. 5c.The spacing of the ripples in frequency obviously permit the 5microsecond time to be determined accurately and unequivocally. Areasonable observer could also be sure enough about the 0.5 microsecondtime difference. But it is apparent that convincing evaluation of a 0.2microsecond time difference would call for a more sophisticated analysisor a wider bandwidth.

The autocorrelation function and the power spectrum are Fouriertransform pairs, so that they should contain equivalent information. Butthere are important differences in the way they contain thisinformation. The autocorrelation function has a very strong ability tosmooth over irregularities in the signal. Possibly the slight wavinessin the autocorrelation function (FIG. 7) could be analyzed to extractthe time delay.

The spectrum, on the other hand, establishes a better distinctionbetween the echo and the extraneous features, so that the latter can befiltered out. Thus, processing involving spectrum calculation seemsdesirable and conversion of the signal to digital form seems to be thesurest way to accomplish the processing. Furthermore, importantadditional benefits can be realized through the versatility of digitalprocessing.

An attractive way of extracting the time delay has been given the name"cepstrum" (from "spectrum" partly turned around). After the spectrum iscomputed, its logarithm is taken and then another Fourier transform istaken. Echos stand out as sharp peaks in the second transform, providedthat the signal-to-noise ratio of the original signal is high enough.Just how high will be considered below.

It should be noted that yet another logarithmic operation may beemployed. An analog logarithmic operation on the incoming signal will beadvantageous in reducing the dynamic range that subsequent stages haveto accommodate. Such an analog compression before conversion to digitalform does not supplant the subsequent logarithmic operation in thefrequency domain in the calculation of the cepstrum; it eases theresolution demands on the analog-to-digital converter.

The signal-to-noise requirements for extracting time delays by cepstrumprocessing indicate that good results are possible down to an SNR of 0dB or even lower when suitable windows (filters) are used for thecharacteristics of the signal and noise. In general, the bandwidthshould be at least several times the reciprocal of the time delay, asone would expect from FIG. 5.

The design of a signal-to-noise ratio of at least 10 dB and preferably20 dB will be as close to being correct as any estimate that can be madeof SNR. The time window should minimize the intake of noise when thereis no signal but must not unfairly abbreviate the delay signal relativeto the direct signal.

Because lightning is a strong signal, the truncation error of theanalog-to-digital converter (ADC) can be the dominant signal uncertaintyor "noise". Thermal noise is not likely to be important and receivernoise can be made even smaller than thermal noise. The ADC "noise" islargely a question of the cost of the converter.

The sampling rate required for the system of the present inventionfollows rather directly from the desire to measure time delays down to0.5 microseconds. The corresponding fringes in the power spectrum willhave a spacing of 2 MHz and at least three complete fringes seems to bean ungenerous but tolerable minimum number of fringes upon which to basethe determination. Thus, a signal bandwidth of 6 MHz is specified. Thesampling theorem requires a minimum sampling rate of 12 megasamples persecond, but all experience teaches that a liberal factor of safety isneeded to obtain sound results in the presence of significant noise.Therefore, a sampling rate of 36 Ms/s is preferred.

This factor of safety and sampling rate is a primal requirement forhaving data worth processing. For a given sampling rate, the cost of theanalog-to-digital converter rises rapidly with the number of bits ofaccurate resolution that it must provide. An estimate of this resolutionwill now be made.

If all direct signals had the same magnitude, the signal-to-noise powerratio for the echo would be approximately (2^(n))², reduced further bythe square of A1 (the relative strength of the echo, if notsubstantially equal to unity), where n is the number of bits. Although a20 dB signal-to-noise ratio should be sufficient when the signal has theoptimum amplitude, it is probably necessary to allow another 30 dB forsignal level variations even when a compressive circuit precedes theADC. Another 10 dB is appropriate to allow for fairly strong waves(i.e., A1=0.32). The total is 60 dB, so that the above quantity shouldbe set equal to one million.

The solution in this case for n is 10 bits. Thus, a 10-bit ADC with a 36MHz sampling rate is preferred. Single chips with this capability arebecoming available at gradually decreasing prices.

A memory-less logarithmic amplifier characteristic is obtainable atthese frequencies by placing Schottky-diode limiters between some of thefinal gain stages preceding the ADC. Logarithmic amplifiers usingavailable fast transistors could accomplish the compression withsufficienty low distortion. The anticipated signals will vary enough instrength from variations in distance to make this compression of dynamicrange appropriate. By reducing the dynamic range from 30 dB to 10 dB,one might hope to increase the signal-to-noise ratio sufficiently topermit much swifter short cuts in place of the cepstrum processing.

Experiments have been conducted on natural lightning utilizing aground-based antenna incorporating a delay line to introduce a pathdifference of 0.2 microseconds. The spectrum of the combined signalclearly reveals the presence of the multipath, as shown in FIG. 6. Thespectrum has substantial power frequencies irrelevant to the intentionalmultipath, but the spectrum analysis segregates the interferring signals(which dominate the raw waveform) from the desired signal that appearsat the expected frequencies of 5 MHz and 10 MHz, which will indicate atime delay of 0.2 microseconds after a further Fourier transform inaccordance with the cepstrum prescription. The peak at 6 MHz is asystematic artifact of the system (present in the absence of timedelay). Such an artifact can be removed digitally at this stage on thebasis of prior calibration.

As stated above, the autocorrelation function theoretically containsexactly the same information as the power spectrum. However, theautocorrelation calculation on the same stored waveform utilized in FIG.6 lacks distinctive features that can be attributed to the multipath.The autocorrelation calculation produces a very sharply defined result,so that the minor waves in the curve of FIG. 7 may in principle containextractable information on both the echo and the interference.

The electronics of the system of the present invention include areceiver, signal processing equipment, and display. It is likely thatthe receiver will be analog in its first stages and that the signalprocessing will at some point become digital. A way to obtain aninexpensive receiver with about the right signal bandwidth and more thanthe required tunability is to use the receiver components mass-producedfor television and video-tape recorders. Television usesvestigial-sideband reduced-carrier modulation. The reduced carrier is,nevertheless, the most prominent characteristic of the received signalas viewed on a spectrum analyzer and is necessary for the operation ofthe detector that converts the intermediate frequency signal to thebaseband video signal. Lightning does not come with a carrier. Thiscondition can be dealt with by adding a carrier, generated by a localoscilator, at almost any point up to the input to the detector. Thetelevision interface of a personal computer provides enough carrierpower to activate the detector. Alternatively, the detector could bereplaced by a true mixer to shift the received signal to or nearbaseband. A second local oscilator would still be required. Eitherarrangement is capable of preserving the echo information.

Signal processing will operate on the baseband signal. In theory, thebandlimited signal could be sampled directly, without conversion tobaseband, but such an arrangement would place excessive demands on theperfection of the sampling characteristics of the ADC.

A block diagram of the system of the present invention is shown in FIG.8. A combined block 10 of mixer, tunable local oscillator,intermediate-frequency amplifier, and detector is the front end of atelevision receiver. One might even consider using the picture tube anddeflection circuits of a small screen television set as a display unit12. In effect, the signal is detoured through a computer, thearrangement otherwise resembling a television set. It is unlikely thatthe limiter, the preamplifier, and the compressive circuit will beadapted from television accessories; suitable circuits can beconstructed from inexpensive semiconductor devices.

The use of digital processing permits the characteristics of a simplediode compression circuit to be stored and allowed for in thecalculations. The microcomputer 14 may either be a complete system forprototype testing or simply microprocessor chips which would not needkeyboards or disc drives. Experiments have shown that very satisfactoryanalog-to-digital conversion is technically possible in reasonably smallpackages. Generally, requirements for many bits of resolution greatlyincrease the cost of the analog-to-digital converter 16. Analogcompression before the ADC 16 is expected to keep the bit requirementsfrom expanding unduly as signals of widely varying strengths areencountered. The ADC 16 requires resolution, speed and reasonablemonotonicity, but not absolute accuracy because consistent errors can beaccounted for in the same way that allowances made for thecharacteristics of the analog compressive circuits.

The bandwidth required to derive lightning range by multipathinterference is comparable to that used in television. The interferenceeffect that is exploited in this determination would be very pronouncedover water. When the water is the sea, the altitude of the reflectingsurface will be known exceedingly well and the altitude of the aircraftshould be known with good accuracy. The approximate formula for rangehas been shown to hold well enough over most of the ranges of interestto be used for error estimation. It indicates that the relative error inrange will be essentially the same as the relative error in estimatingthe height of the cloud discharge.

As stated above, the height of the lightning source can be estimatedbefore a flight from climatological data and it is expected that thisestimate can be further refined in real time from the prevailingmeteorological data available from the routine radiosonde measurementsand on-board instruments.

The interference effect will not be as strong over land and the altitudeof the reflecting land surface will be needed to compute the range. Thisinformation is available to the pilot and can be entered into theinstrument.

It is thus seen that the objects of this invention have been achieved inthat there has been disclosed a lightning ranging system for estimatingthe distance from an airborne or elevated object to a lightningdischarge utilizing but a single antenna. The spectrum of the receiveddirect/reflected path signal is analyzed (cepstrum processing) todetermine the time delay between the direct and reflected signals. Thistime delay along with the altitudes of the lightning discharge and theairborne object, are utilized to compute the range to the lightningdischarge with the program of Appendix A. The bandwidth requirements ofthe present system are such that conventional television components canbe utilized. The present system eliminates the inherent limitations bothof radar and of the known Stormscope device.

It is recognized that modifications and variations of the presentinvention will occur to those skilled in the art and it is intended thatall such modifications and variations be included within the scope ofthe appended claims.

Appendix A: Program for Propagation Calculations

The variables used to represent quantities in the program are defined inthe program. They are single characters followed (at most) by a singlenumber. This restriction makes them acceptable to any BASIC interpreter.However, it also makes them harder to identify, so a table of symbols isgiven below in addition to the identification in program remarks.

The program is written in BASIC which differs from ANSI standard minimalBASIC in having more than one statement on some of the lines, with acolon as a separator. It will run as written on most personal computers,including all Commodore models before the Amiga. Some Hewlett-PackardBASICs require a "@" in place of the colon and VAX/VMS BASIC calls for aback-slash instead of a colon.

Enough unused line numbers are present so that the program can bewritten with one statement per line, as required for some versions ofBASIC.

Statements can be added in the usual way to cause the calculation toloop on successive values of grazing angle and other variables. Also,additional statements are usually needed to direct the output to aprinter. The print statements can be rewritten to produce tables in anydesired form.

The calculations are sufficiently rapid that there is little advantagein bypassing the calculation of results that are not wanted in a table,especially in view of the fact that some of the calculated quantitiesare used in subsequent calculations.

"Scratch variables" are intermediates in calculations and are the onlyone that may be reused; all of the others retain their assigned values.Range is converted to nautical miles in the PRINT statement.

Symbol Table

    ______________________________________                                        A    radians on 4/3 earth from source to reflection point                     A1   magnitude of reflection, horizontal polarization, smooth sea.            A2   ibid., rough sea                                                         A3   ibid., vertical polarization, smooth sea                                 A4   ibid., rough sea (nominal, not plotted)                                  B    radians on 4/3 earth from reflection point to receiver                   C    cosine of the grazing angle                                              D    range at sea level, feet                                                 D1   divergence power reduction factor                                        E1   relative dielectric constant of sea water (real part)                    F    frequency in megahertz                                                   G    grazing angle in radians                                                 G1   grazing angle in degrees                                                 H    average height of source and receiver, feet                              H1   height of source, feet                                                   H2   height of receiver, feet                                                 I0   ionospheric reflection path difference, feet                             I9   ionospheric height, feet                                                 L    direct path from source to receiver over 4/3 earth, feet                 N    half-angle of range on true earth, radians                               O    scratch variable                                                         O2   roughness factor, power ratio                                            P    scratch variable                                                         P0   path difference, feet                                                    P9   approximate path difference, feet                                        Q    scratch variable                                                         R    4/3 earth radius, feet                                                   R0   true earth radius, feet                                                  R1   path length from source to reflection point, feet                        R2   path length from reflection point to receiver, feet                      S    sine of the grazing angle                                                S1   conductivity of the sea, mhos/meter                                      U,V  scratch variables                                                        W1   peak-to trough wave height, feet                                         W    root-mean-square wave height, meters                                     X,Y  scratch variables                                                        10   REM PATH                                                                 110  P5=1.57079633:REM PI/2                                                   120  R=280 2:R0=.75*R:REM 4/3 & 1.0 EARTH RADII, FT                           130  E1=80:REM DIELECTRIC CONSTANT                                            140  S1=4: REM CONDUCTIVITY, MHOS/M                                           160  F=60:REM FREQUENCY, MHZ                                                  170  W1=20:REM PEAK-TO-TROUGH WAVE HEIGHT, FT                                 180  I9=2E5: REM IONOSPHERE HEIGHT, FT                                        190  :                                                                        200  G1= 6:REM GRAZING ANGLE, DEGREES                                         210  G=P5*G1/90:C=COS(G):S=SIN(G)                                             220  REM ROUGHNESS FACTOR, POWER RATIO                                        230  W= .0644*W1:O=8*P5*S*W*F/300:O2=EXP(-O 2)                                240  :                                                                        250  REM REFLECTIVITY, POWER RATIO                                            260  X=18000*S1/F:Y=E1-C*C                                                    270  P=SQR(Y*Y+X*X):Q=S*SQR(2*(Y+P))                                          280  P=P+S*S:G2=(P-Q)/(P+Q): REM HORIZ. POL.                                  285  U=(E1*E1+X*X)*S+P/S                                                      290  V=E1*SQR(2*(P+Y))+X*SQR(2*(P-Y))                                         295  G3=SQR((U-V)/(U+V)):REM VERT. POL.                                       300  :                                                                        310  H1=20000:H2=20000:REM SOURCE AND RECEIVER                                     HEIGHTS, FT                                                              315  :                                                                        320  REM RANGE D AND PATH DIFFERENCE P0, FT                                   330  Y=C/(1+H1/R):X=SQR(1-Y 2):A=P5-G-ATN(Y/X)                                350  R1=SIN(A)*(R+H1)/C                                                       360  Y=C/(1+H2/R):X=SQR(1-Y 2):B=P5-G-ATN(Y/X)                                380  R2=SIN(B)*(R+H2)/C                                                       390  L=((R+H1)*COS(A)-(R+H2)*COS(B)) 2                                        400  L=SQR(L+((R+H1)*SIN(A)+(R+H2)*SIN(B)) 2)                                 410  P0= R1+R2-L:D=(A+B)*R                                                    450  :                                                                        460  P9=2*H1*H2/D:REM APPROX. PATH DIFF., FT.                                 500  :                                                                        510  D1=1/SQR(1+2*R1*R2*C/D/R/S):REM DIVERGENCE                                    FACTOR                                                                   515  :                                                                        520  REM VOLTAGE REFLECTION FACTOR                                            530  A1=SQR(D1*G2)/(1+P0/L):A2=A1*SQR(O2):REM                                      HORIZ. POL.                                                              532  A3=SQR(D1*G3)/(1+P0/L):A4=A3*SQR(O2):REM                                      VERT. POL.                                                               540  :                                                                        550  H=(H1+H2)/2:N=D/R0/2                                                     560  U=(R0+H)*SIN(N):V=I9+R0*(1-COS(N))                                       570  I0=2*(SQR(V*V+U*U)-U):REM IONOSPHERIC PATH                                    DIFF., FT.                                                               600  PRINT "GRAZING ANGLE,H1,H2 = ";G1;H1,H2                                  700  PRINT "PATH DIFF, FT = ";INT(P0+.5)                                      710  PRINT "RANGE,NM = ";.1*INT(D/607.6)                                      720  PRINT "DIVERGENCE FACTOR = ";                                                 .0001*INT(10000*D1)                                                      730  PRINT "REFLEC. PWR. COEF (H) = ";                                             .0001*INT(10000*G2)                                                      735  PRINT "REFLEC. PWR. COEF (V) = ";                                             .0001*INT(10000*G3)                                                      740  PRINT "SMOOTH ECHO VOLTAGE RATIO (H) = ";                                     .0001*INT(10000*A1)                                                      745  PRINT "SMOOTH ECHO VOLTAGE RATIO (V) = ";                                     .0001*INT(1000*A3)                                                       750  PRINT"ROUGHNESS FACTOR FOR";W1;"FT                                            WAVES = ";.0001*INT(10000*O2)                                            760  PRINT "ROUGH ECHO VOLTAGE RATIO (H) = ";                                      .0001*INT(10000*A2)                                                      765  PRINT "ROUGH ECHO VOLTAGE RATIO (V) = ";                                      .0001*INT(10000*A4)                                                      770  PRINT "APPROX. PATH DIFF., FT = ";INT(P9+.5)                             780  PRINT " IONOSPHERIC DELAY, FT = "; INT(I0)                               800  PRINT:END                                                                READY.                                                                        ______________________________________                                    

What is claimed is:
 1. Interferometric lightning ranging system fordetermining distance between a lightning discharge at a first altitudeand an airborne or elevated object at a second altitude comprising:areceiver on the object adapted to receive electromagnetic radiationsignals generated by a lightning discharge along both a direct and asurface reflected path, the receiver having a center frequency of atleast 30 MHz; signal processing means interconnected with the receiverfor determining in the frequency domain the difference in time ofarrival of the direct and reflected signals from the interferencepattern between the direct and reflected signals; and computing means ofcalculating the distance from the difference in the time of arrival ofthe direct and reflected signals.
 2. The system of claim 1 wherein thesignal processing means is adapted to analyze ripples in the spectrum ofthe received signal, the spacing of the ripples being an indication ofthe difference in the time of arrival.
 3. The system of claim 2 whereinthe signal processing means is digital.
 4. The system of claim 3 whereinthe signal processing means includes an analog-to-digital converter. 5.The system of claim 3 in which the signal processing means includesmeans to:(1) compute the spectrum; (2) take the logarithm of thespectrum; and (3) take the Fourier transform of the logarithm of thespectrum, the Fourier transform including sharp peaks indicating thedifference in time of arrival.
 6. The system of claim 4 wherein ananalog signal compression operation precedes conversion to digital formin the analog-to-digital converter.
 7. The system of claim 4 wherein theanalog-to-digital converter has at least a 20 MHz sampling rate and aresolution of at least 10 bits.
 8. The system of claim 6 wherein amemory-less logarithm amplifier performs the signal compressionoperation.
 9. The system of claim 1 wherein the receiver has a centerfrequency of at least 30 MHz and a bandwidth of at least 4 MHz.
 10. Thesystem of claim 1 further including an antenna connected to thereceiver, the antenna comprising a loop lying approximately in thehorizontal plane.
 11. The system of claim 1 further including antennameans connected to the receiver, the antenna means comprisingcombinations of horizontal monopoles.
 12. The system of claim 1 furtherincluding antenna means connected to the receiver, the antenna meanscomprising combinations of horizontal dipoles.
 13. The system of claim 3in which the signal processing means includes means to compute theautocorrelation function of the received signal, variations in theautocorrelation function being indicative of the time delay.
 14. Thesystem of claim 1 including means for storing calibration data obtainedby exposing the system to a signal without path difference to correctfalse echo indications from system imperfections.